As Na is a count of the number of (atoms/molecules) in a mole of a substance, the shape of the mole seems (to me, at least) to be irrelevant. You can have a mole that is a "flat pancake", or a mole that is a cube, or a mole that is a sphere - doesn't matter - as long as you have a mole. So the "perfect cube" requirement ("Third, the value chosen..." above) seems (again, to me) "bogus", and should be discarded??